# importing all required lib for the Project

import numpy as np
import pandas as pd
import seaborn as sns
import scipy.stats as stats
import matplotlib.pyplot as plt
%matplotlib inline

PART 1

Question 1:

1.Refer to the above table and find the joint probability of the people who planned to purchase and actually placed an order.

2.Refer to the above table and find the joint probability of the people who planned to purchase and actually placed an order, given that people planned to purchase.

#Sol 1:
A = 400/2000
#Sol2:
B = (400/2000)/(500/2000)
print('Answer for 1st question',A)
print('Answer for 2nd question',B)

Answer for 1st question 0.2
Answer for 2nd question 0.8

Question: 2

An electrical manufacturing company conducts quality checks at specified periods on the products it manufactures. Historically, the failure rate for the manufactured item is 5%. Suppose a random sample of 10 manufactured items is selected. Answer the following questions.

A. Probability that none of the items are defective?

B. Probability that exactly one of the items is defective?

C. Probability that two or fewer of the items are defective?

D. Probability that three or more of the items are defective ?

## Question 2 falls under Biomial distibution
## Success rate is 0.95
## Failure rate is 0.05
## Sample n = 10
k1=0 # Zero defects
k2=1 # Exactly one defects
k3=[0,1,2] # two or fewer defects
k4=np.arange(3,11) # three or more defects
n=10
p=0.05

binomial1 = stats.binom.pmf(k1,n,p)
binomial2 = stats.binom.pmf(k2,n,p)
binomial3 = stats.binom.pmf(k3,n,p)
binomial4 = stats.binom.pmf(k4,n,p)

print('Probability that none of the items are defective',round(binomial1,4))
print('Probability that exactly one of the items are defective',round(binomial2,4))
print('Probability that two or fewer of the items are defective',round(sum(binomial3),4))
print('Probability that three or more of the items are defective',round(1-sum(binomial3),4))

Probability that none of the items are defective 0.5987
Probability that exactly one of the items are defective 0.3151
Probability that two or fewer of the items are defective 0.9885
Probability that three or more of the items are defective 0.0115

Question:3

A car salesman sells on an average 3 cars per week.

A. Probability that in a given week he will sell some cars.

B. Probability that in a given week he will sell 2 or more but less than 5 cars.

C. Plot the poisson distribution function for cumulative probability of cars sold per-week vs number of cars sold perweek.

# Question 3 falls under Poisson distribution
rate = 3
n0=0 #no cars he sell in a week
poisson_0 = stats.poisson.pmf(n0,rate)
n1=1-poisson_0 # in a week sells some cars i.e, 1 or more cars
n2=[2,3,4] #he will sell 2 or more but less than 5 cars.
poisson1 = n1
poisson2 = stats.poisson.pmf(n2,rate)

print('A) Probability that in a given week he will sell some cars is', round(poisson1,4))
print('B) Probability that in a given week he will sell 2 or more but less than 5 cars is',round(sum(poisson2),4))

A) Probability that in a given week he will sell some cars is 0.9502
B) Probability that in a given week he will sell 2 or more but less than 5 cars is 0.6161

n3=np.arange(0,18)
poisson_cdf = stats.poisson.cdf(n3,rate)

poisson_pmf = stats.poisson.pmf(n3,rate)

plt.plot(poisson_cdf,poisson_pmf, 'g*-')
plt.title('C) cumulative probability of cars sold per-week vs number of cars sold perweek')
plt.xlabel('CDF')
plt.ylabel('PMF')
plt.show()

C:\Users\Prem\anaconda3\lib\site-packages\matplotlib\backends\backend_agg.py:238: RuntimeWarning: Glyph 2 missing from current font.
  font.set_text(s, 0.0, flags=flags)
C:\Users\Prem\anaconda3\lib\site-packages\matplotlib\backends\backend_agg.py:201: RuntimeWarning: Glyph 2 missing from current font.
  font.set_text(s, 0, flags=flags)

Question: 4

Accuracy in understanding orders for a speech based bot at a restaurant is important for the Company X which has designed, marketed and launched the product for a contactless delivery due to the COVID-19 pandemic. Recognition accuracy that measures the percentage of orders that are taken correctly is 86.8%. Suppose that you place order with the bot and two friends of yours independently place orders with the same bot. Answer the following questions.

A. What is the probability that all three orders will be recognised correctly?

B. What is the probability that none of the three orders will be recognised correctly?

C. What is the probability that at least two of the three orders will be recognised correctly?

#Question 4 falls under binomial distribution

p1=0.868 
n1=3
k5=np.arange(0,4)

binomial5 = stats.binom.pmf(k5,n1,p1)

print('A) All the three orders will be recognised correctly is %1.4f' %binomial5[3])
print('B) None orders will be recognised correctly is %1.4f' %binomial5[0])
print('C) At least two of the three orders will be recognised correctly is %1.4f' %(1-(binomial5[0]+binomial5[1])))

A) All the three orders will be recognised correctly is 0.6540
B) None orders will be recognised correctly is 0.0023
C) At least two of the three orders will be recognised correctly is 0.9523

Question:5

A group of 300 professionals sat for a competitive exam. The results show the information of marks obtained by them have a mean of 60 and a standard deviation of 12. The pattern of marks follows a normal distribution. Answer the following questions.

A. What is the percentage of students who score more than 80.

B. What is the percentage of students who score less than 50.

C. What should be the distinction mark if the highest 10% of students are to be awarded distinction?

# Normal Distribution

mean = 60
std = 12
Norm=stats.norm.cdf(80,loc=mean,scale=std)

M= 1- Norm

N=stats.norm.cdf(50,loc=mean,scale=std)

#p(z>= (x-60)/12)=0.10 # We know the percentage and we need to find the marks
#using Z-score table for 0.9 is 1.282
#(X-60)/12=1.282
O=(1.282*12)+60

print(' A) Percentage of students who score more than 80 is %1.4f' % M)
print(' B) Percentage of students who score less than 50 is %1.4f' % N)
print(' C) Distinction mark if the highest 10% of students are to be awarded distinction is',O)

 A) Percentage of students who score more than 80 is 0.0478
 B) Percentage of students who score less than 50 is 0.2023
 C) Distinction mark if the highest 10% of students are to be awarded distinction is 75.384

Question:6

Explain 1 real life industry scenario [other than the ones mentioned above] where you can use the concepts learnt in this module of Applied statistics to get a data driven business solution

There are some of the examples to explain the role of statistic in real life.

1) Medical Study

Statistics are used behind all the medical study. Statistic help doctors keep track of where the baby should be in his/her mental development. Physician’s also use statistics to examine the effectiveness of treatments.

2) Weather Forecasts

Statistics are very important for observation, analysis and mathematical prediction models. Weather forecast models are built using statistics that compare prior weather conditions with current weather to forecast future weather conditions.

3) Quality Testing

A company makes thousands of products every day and make sure that they sold the best quality items. For a company it is not possible to test each product. So the company uses quality test with the help of statistics.

4) Stock Market

The stock market also uses statistical computer models for stock analysis. Stock analysts get the information about economy using statistics concepts.

5) Consumer Goods

Retailers keeps track of everything they sell and to know the stock using statistics. Worldwide leading retailers use statistics to calculate what products ship to each store and when.

PART 2

PROJECT BASED

ATTRIBUTE INFORMATION:

1. Team: Team’s name
2. Tournament: Number of played tournaments.
3. Score: Team’s score so far.
4. PlayedGames: Games played by the team so far.
5. WonGames: Games won by the team so far.
6. DrawnGames: Games drawn by the team so far.
7. LostGames: Games lost by the team so far.
8. BasketScored: Basket scored by the team so far.
9. BasketGiven: Basket scored against the team so far.
10. TournamentChampion: How many times the team was a champion of the tournaments so far.
11. Runner-up: How many times the team was a runners-up of the tournaments so far.
12. TeamLaunch: Year the team was launched on professional basketball.
13. HighestPositionHeld: Highest position held by the team amongst all the tournaments played.

#Since the data set has not defined NaN format. We can make '-' as NaN 
missing_values=['-']
BBdata= pd.read_csv('C:\\Users\\Prem\\Favorites\\DS - Part2 - Basketball (1).csv',na_values=missing_values)
BBdata.head(10)

	Team	Tournament	Score	PlayedGames	WonGames	DrawnGames	LostGames	BasketScored	BasketGiven	TournamentChampion	Runner-up	TeamLaunch	HighestPositionHeld
0	Team 1	86	4385.0	2762.0	1647.0	552.0	563.0	5947.0	3140.0	33.0	23.0	1929	1
1	Team 2	86	4262.0	2762.0	1581.0	573.0	608.0	5900.0	3114.0	25.0	25.0	1929	1
2	Team 3	80	3442.0	2614.0	1241.0	598.0	775.0	4534.0	3309.0	10.0	8.0	1929	1
3	Team 4	82	3386.0	2664.0	1187.0	616.0	861.0	4398.0	3469.0	6.0	6.0	1931to32	1
4	Team 5	86	3368.0	2762.0	1209.0	633.0	920.0	4631.0	3700.0	8.0	7.0	1929	1
5	Team 6	73	2819.0	2408.0	990.0	531.0	887.0	3680.0	3373.0	1.0	4.0	1934-35	1
6	Team 7	82	2792.0	2626.0	948.0	608.0	1070.0	3609.0	3889.0	NaN	NaN	1929	3
7	Team 8	70	2573.0	2302.0	864.0	577.0	861.0	3228.0	3230.0	2.0	3.0	1929	1
8	Team 9	58	2109.0	1986.0	698.0	522.0	766.0	2683.0	2847.0	NaN	1.0	1939-40	2
9	Team 10	51	1884.0	1728.0	606.0	440.0	682.0	2159.0	2492.0	1.0	NaN	1932-33	1

BBdata.describe(include='all')

	Team	Tournament	Score	PlayedGames	WonGames	DrawnGames	LostGames	BasketScored	BasketGiven	TournamentChampion	Runner-up	TeamLaunch	HighestPositionHeld
count	61	61.000000	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000	9.000000	13.000000	61	61.000000
unique	61	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	47	NaN
top	Team 18	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1929	NaN
freq	1	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	10	NaN
mean	NaN	24.000000	916.450000	810.100000	309.033333	192.083333	308.816667	1159.350000	1159.233333	9.666667	6.615385	NaN	7.081967
std	NaN	26.827225	1138.342899	877.465393	408.481395	201.985508	294.508639	1512.063948	1163.946914	11.618950	8.109033	NaN	5.276663
min	NaN	1.000000	14.000000	30.000000	5.000000	4.000000	15.000000	34.000000	55.000000	1.000000	1.000000	NaN	1.000000
25%	NaN	4.000000	104.250000	115.500000	34.750000	26.250000	62.750000	154.500000	236.000000	1.000000	1.000000	NaN	3.000000
50%	NaN	12.000000	395.500000	424.500000	124.000000	98.500000	197.500000	444.000000	632.500000	6.000000	4.000000	NaN	6.000000
75%	NaN	38.000000	1360.500000	1345.500000	432.750000	331.500000	563.500000	1669.750000	2001.250000	10.000000	7.000000	NaN	10.000000
max	NaN	86.000000	4385.000000	2762.000000	1647.000000	633.000000	1070.000000	5947.000000	3889.000000	33.000000	25.000000	NaN	20.000000

BBdata.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 61 entries, 0 to 60
Data columns (total 13 columns):
 #   Column               Non-Null Count  Dtype  
---  ------               --------------  -----  
 0   Team                 61 non-null     object 
 1   Tournament           61 non-null     int64  
 2   Score                60 non-null     float64
 3   PlayedGames          60 non-null     float64
 4   WonGames             60 non-null     float64
 5   DrawnGames           60 non-null     float64
 6   LostGames            60 non-null     float64
 7   BasketScored         60 non-null     float64
 8   BasketGiven          60 non-null     float64
 9   TournamentChampion   9 non-null      float64
 10  Runner-up            13 non-null     float64
 11  TeamLaunch           61 non-null     object 
 12  HighestPositionHeld  61 non-null     int64  
dtypes: float64(9), int64(2), object(2)
memory usage: 6.3+ KB

BBdata.isnull().sum()

Team                    0
Tournament              0
Score                   1
PlayedGames             1
WonGames                1
DrawnGames              1
LostGames               1
BasketScored            1
BasketGiven             1
TournamentChampion     52
Runner-up              48
TeamLaunch              0
HighestPositionHeld     0
dtype: int64

# Function to calculate missing values by column
def missing_values_table(df):
        # Total missing values
        mis_val = df.isnull().sum()
        
        # Percentage of missing values
        mis_val_percent = 100 * df.isnull().sum() / len(df)
        
        # Make a table with the results
        mis_val_table = pd.concat([mis_val, mis_val_percent], axis=1)
        
        # Rename the columns
        mis_val_table_ren_columns = mis_val_table.rename(
        columns = {0 : 'Missing Values', 1 : '% of Total Values'})
        
        # Sort the table by percentage of missing descending
        mis_val_table_ren_columns = mis_val_table_ren_columns[
            mis_val_table_ren_columns.iloc[:,1] != 0].sort_values(
        '% of Total Values', ascending=False).round(1)
        
         # Print some summary information
        print ("Your selected dataframe has " + str(df.shape[1]) + " columns.\n"      
            "There are " + str(mis_val_table_ren_columns.shape[0]) +
              " columns that have missing values.")
        
        # Return the dataframe with missing information
        return mis_val_table_ren_columns

missing_values_table(BBdata)

Your selected dataframe has 13 columns.
There are 9 columns that have missing values.

	Missing Values	% of Total Values
TournamentChampion	52	85.2
Runner-up	48	78.7
Score	1	1.6
PlayedGames	1	1.6
WonGames	1	1.6
DrawnGames	1	1.6
LostGames	1	1.6
BasketScored	1	1.6
BasketGiven	1	1.6

There are 85.2% missing value in TournamentChampion & 78.7% in Runner-Up. So,drop that columns in the data set. Rest are small percentage of missing values. So, it can be filled with mean of the columns

##copying the df to another df

BBdata1 = BBdata.copy()

BBdata1.drop('TournamentChampion',axis=1,inplace=True)

BBdata1.drop('Runner-up',axis=1,inplace=True)

BBdata1['Score'].fillna(BBdata1.Score.mean(),inplace=True) # fill miss value with mean. 

BBdata1['PlayedGames'].fillna(BBdata1.PlayedGames.mean(),inplace=True)


BBdata1['WonGames'].fillna(BBdata1.WonGames.mean(),inplace=True)


BBdata1['DrawnGames'].fillna(BBdata1.DrawnGames.mean(),inplace=True)


BBdata1['LostGames'].fillna(BBdata1.LostGames.mean(),inplace=True)


BBdata1['BasketScored'].fillna(BBdata1.BasketScored.mean(),inplace=True)


BBdata1['BasketGiven'].fillna(BBdata1.BasketGiven.mean(),inplace=True)

#changing the float type to int
BBdata1 = BBdata1.astype({"Score":'int', "PlayedGames":'int',"WonGames":'int',"DrawnGames":'int',
                          "LostGames":'int',"BasketScored":'int',"BasketGiven":'int'}) 

#Final dataset will null zero
BBdata1 = BBdata1.drop(BBdata1.index[60])

Univariate Analysis

UD = BBdata1['PlayedGames']
len(UD)

60

UD.isnull().sum()

0

plt.hist(UD, bins=40)

(array([12.,  7.,  4.,  2.,  2.,  4.,  3.,  0.,  2.,  3.,  1.,  0.,  0.,
         0.,  1.,  1.,  0.,  2.,  1.,  0.,  2.,  2.,  0.,  0.,  2.,  0.,
         0.,  0.,  1.,  0.,  0.,  0.,  0.,  1.,  1.,  0.,  0.,  1.,  2.,
         3.]),
 array([  30. ,   98.3,  166.6,  234.9,  303.2,  371.5,  439.8,  508.1,
         576.4,  644.7,  713. ,  781.3,  849.6,  917.9,  986.2, 1054.5,
        1122.8, 1191.1, 1259.4, 1327.7, 1396. , 1464.3, 1532.6, 1600.9,
        1669.2, 1737.5, 1805.8, 1874.1, 1942.4, 2010.7, 2079. , 2147.3,
        2215.6, 2283.9, 2352.2, 2420.5, 2488.8, 2557.1, 2625.4, 2693.7,
        2762. ]),
 <BarContainer object of 40 artists>)

sns.distplot(UD)

C:\Users\Prem\anaconda3\lib\site-packages\seaborn\distributions.py:2557: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

<AxesSubplot:xlabel='PlayedGames', ylabel='Density'>

plt.gcf().set_size_inches(10,3)
sns.boxplot(BBdata1['PlayedGames'],color='g');

C:\Users\Prem\anaconda3\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

sns.violinplot(UD) 

C:\Users\Prem\anaconda3\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

<AxesSubplot:xlabel='PlayedGames'>

plt.figure(figsize=(20,10)) # makes the plot wider
plt.hist(UD, color='g') # plots a simple histogram
plt.axvline(UD.mean(), color='m', linewidth=3)
plt.axvline(UD.median(), color='b', linestyle='dashed', linewidth=3)
plt.axvline(UD.mode()[0], color='r', linestyle='dashed', linewidth=3)

<matplotlib.lines.Line2D at 0x263610213d0>

Multivariate analysis

sns.pairplot(BBdata1, kind='reg')

<seaborn.axisgrid.PairGrid at 0x26364578460>

BBdata1.cov()

	Tournament	Score	PlayedGames	WonGames	DrawnGames	LostGames	BasketScored	BasketGiven	HighestPositionHeld
Tournament	722.782768	3.003033e+04	2.355925e+04	10671.614124	5372.170904	7516.715537	3.962956e+04	3.090991e+04	-101.172034
Score	30030.333051	1.295825e+06	9.785666e+05	463704.696610	220292.385593	294612.626271	1.715454e+06	1.250509e+06	-4049.124576
PlayedGames	23559.249153	9.785666e+05	7.699455e+05	346774.216949	176166.940678	247031.154237	1.286941e+06	1.011131e+06	-3316.361017
WonGames	10671.614124	4.637047e+05	3.467742e+05	166857.049718	77508.658192	102428.853672	6.172252e+05	4.401460e+05	-1406.527119
DrawnGames	5372.170904	2.202924e+05	1.761669e+05	77508.658192	40798.145480	57867.608757	2.877725e+05	2.333322e+05	-773.258475
LostGames	7516.715537	2.946126e+05	2.470312e+05	102428.853672	57867.608757	86735.338701	3.820110e+05	3.376645e+05	-1136.736441
BasketScored	39629.558475	1.715454e+06	1.286941e+06	617225.191525	287772.461864	382010.997458	2.286337e+06	1.638664e+06	-5213.356780
BasketGiven	30909.909040	1.250509e+06	1.011131e+06	440145.958192	233332.166667	337664.535028	1.638664e+06	1.354772e+06	-4499.689831
HighestPositionHeld	-101.172034	-4.049125e+03	-3.316361e+03	-1406.527119	-773.258475	-1136.736441	-5.213357e+03	-4.499690e+03	28.251695

BBdata1.corr()

	Tournament	Score	PlayedGames	WonGames	DrawnGames	LostGames	BasketScored	BasketGiven	HighestPositionHeld
Tournament	1.000000	0.981258	0.998683	0.971749	0.989295	0.949350	0.974867	0.987781	-0.708002
Score	0.981258	1.000000	0.979687	0.997232	0.958090	0.878780	0.996634	0.943801	-0.669215
PlayedGames	0.998683	0.979687	1.000000	0.967486	0.993972	0.955925	0.969970	0.990020	-0.711065
WonGames	0.971749	0.997232	0.967486	1.000000	0.939416	0.851436	0.999312	0.925745	-0.647819
DrawnGames	0.989295	0.958090	0.993972	0.939416	1.000000	0.972786	0.942234	0.992479	-0.720248
LostGames	0.949350	0.878780	0.955925	0.851436	0.972786	1.000000	0.857843	0.985041	-0.726172
BasketScored	0.974867	0.996634	0.969970	0.999312	0.942234	0.857843	1.000000	0.931079	-0.648672
BasketGiven	0.987781	0.943801	0.990020	0.925745	0.992479	0.985041	0.931079	1.000000	-0.727323
HighestPositionHeld	-0.708002	-0.669215	-0.711065	-0.647819	-0.720248	-0.726172	-0.648672	-0.727323	1.000000

plt.figure(figsize=(10,5))
sns.heatmap(BBdata1.corr(), annot=True, linewidths=.5, fmt= '.2f', center = 1 )  # heatmap
plt.show()

Installing Pandas-Profiling

!pip install pandas-profiling

Collecting pandas-profiling
  Downloading pandas_profiling-3.0.0-py2.py3-none-any.whl (248 kB)
Requirement already satisfied: PyYAML>=5.0.0 in c:\users\prem\anaconda3\lib\site-packages (from pandas-profiling) (5.4.1)
Collecting pydantic>=1.8.1
  Downloading pydantic-1.8.2-cp38-cp38-win_amd64.whl (2.0 MB)
Requirement already satisfied: joblib in c:\users\prem\anaconda3\lib\site-packages (from pandas-profiling) (1.0.1)
Requirement already satisfied: pandas!=1.0.0,!=1.0.1,!=1.0.2,!=1.1.0,>=0.25.3 in c:\users\prem\anaconda3\lib\site-packages (from pandas-profiling) (1.2.4)
Requirement already satisfied: seaborn>=0.10.1 in c:\users\prem\anaconda3\lib\site-packages (from pandas-profiling) (0.11.1)
Requirement already satisfied: jinja2>=2.11.1 in c:\users\prem\anaconda3\lib\site-packages (from pandas-profiling) (2.11.3)
Collecting visions[type_image_path]==0.7.1
  Downloading visions-0.7.1-py3-none-any.whl (102 kB)
Requirement already satisfied: scipy>=1.4.1 in c:\users\prem\anaconda3\lib\site-packages (from pandas-profiling) (1.6.2)
Collecting missingno>=0.4.2
  Downloading missingno-0.5.0-py3-none-any.whl (8.8 kB)
Requirement already satisfied: numpy>=1.16.0 in c:\users\prem\anaconda3\lib\site-packages (from pandas-profiling) (1.20.1)
Requirement already satisfied: matplotlib>=3.2.0 in c:\users\prem\anaconda3\lib\site-packages (from pandas-profiling) (3.3.4)
Collecting htmlmin>=0.1.12
  Downloading htmlmin-0.1.12.tar.gz (19 kB)
Collecting tangled-up-in-unicode==0.1.0
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Use of Pandas Profiling

import pandas_profiling 

pandas_profiling.ProfileReport(BBdata1)

BBdata1.skew()

Tournament             1.197176
Score                  1.574104
PlayedGames            1.123454
WonGames               1.786067
DrawnGames             0.984899
LostGames              0.880596
BasketScored           1.758058
BasketGiven            0.958164
HighestPositionHeld    0.832164
dtype: float64

plt.figure(figsize=(20,20))  # setting the figure size
ax = sns.barplot(x='WonGames', y='Team', data=BBdata1, palette='muted')  # barplot

From the above details. Team 1 has highest performance

PART 3

PROJECT BASED

Description of the attribuites

1. Startup: Name of the company
2. Product: Actual product
3. Funding: Funds raised by the company in USD
4. Event: The event the company participated in
5. Result: Described by Contestant, Finalist, Audience choice, Winner or Runner up
6. OperatingState: Current status of the company, Operating ,Closed, Acquired or IPO

#Since the data set has not defined NaN format. We can make '-' as NaN 
missing_values=['-']
COMdata= pd.read_csv('C:\\Users\\Prem\\Favorites\\DS - Part3 - CompanyX_EU.csv',na_values=missing_values)
COMdata.head(20)

	Startup	Product	Funding	Event	Result	OperatingState
0	2600Hz	2600hz.com	NaN	Disrupt SF 2013	Contestant	Operating
1	3DLT	3dlt.com	$630K	Disrupt NYC 2013	Contestant	Closed
2	3DPrinterOS	3dprinteros.com	NaN	Disrupt SF 2016	Contestant	Operating
3	3Dprintler	3dprintler.com	$1M	Disrupt NY 2016	Audience choice	Operating
4	42 Technologies	42technologies.com	NaN	Disrupt NYC 2013	Contestant	Operating
5	5to1	5to1.com	$19.3M	TC50 2009	Contestant	Acquired
6	8 Securities	8securities.com	$29M	Disrupt Beijing 2011	Finalist	Operating
7	8020 Media	8020media.com	NaN	TC40 2007	Contestant	Operating
8	About Last Night	aboutlastnight.net	NaN	Disrupt NYC 2012	Contestant	Operating
9	Adgregate Markets	adgregate.com	NaN	TC50 2008	Contestant	Operating
10	AdhereTech	adheretech.com	$1.8M	Hardware Battlefield 2014	Contestant	Operating
11	AdRocket	adrocket.com	$1M	TC50 2008	Contestant	Closed
12	Affective Interfaces	affectiveinterfaces.com	NaN	TC50 2009	Contestant	Operating
13	Agrilyst	agrilyst.com	$1M	Disrupt SF 2015	Winner	Operating
14	Aiden	aiden.ai	$750K	Disrupt London 2016	Contestant	Operating
15	AirBoxLab	foobot.io	$17.9K	Hardware Battlefield 2014	Contestant	Operating
16	Aircall	aircall.io	$11.6M	Disrupt SF 2015	Contestant	Operating
17	AirDroids	airdroids.com	$929.2K	Hardware Battlefield 2014	Contestant	Closed
18	AirHelp	airhelp.com	$12.2M	Disrupt NYC 2014	Contestant	Operating
19	AirWander	airwander.com	NaN	Disrupt London 2016	Contestant	Operating

COMdata.shape

(662, 6)

COMdata.dtypes

Startup           object
Product           object
Funding           object
Event             object
Result            object
OperatingState    object
dtype: object

COMdata.isnull().sum()

Startup             0
Product             6
Funding           214
Event              13
Result              0
OperatingState      0
dtype: int64

COMdata1 = COMdata.dropna().copy(deep=True)

COMdata1.shape

(440, 6)

COMdata1.isnull().sum().sum()

0

COMdata1.loc[:,'Funds_in_million'] = COMdata1['Funding'].apply(lambda x: float(x[1:-1])/1000 if x[-1] == 'K' else (float(x[1:-1])*1000 if x[-1] == 'B' else float(x[1:-1])))

COMdata1

	Startup	Product	Funding	Event	Result	OperatingState	Funds_in_million
1	3DLT	3dlt.com	$630K	Disrupt NYC 2013	Contestant	Closed	0.63
3	3Dprintler	3dprintler.com	$1M	Disrupt NY 2016	Audience choice	Operating	1.00
5	5to1	5to1.com	$19.3M	TC50 2009	Contestant	Acquired	19.30
6	8 Securities	8securities.com	$29M	Disrupt Beijing 2011	Finalist	Operating	29.00
10	AdhereTech	adheretech.com	$1.8M	Hardware Battlefield 2014	Contestant	Operating	1.80
...	...	...	...	...	...	...	...
656	Zenefits	zenefits.com	$583.6M	Disrupt NYC 2013	Finalist	Operating	583.60
657	Zivity	zivity.com	$8M	TC40 2007	Contestant	Operating	8.00
659	Zocdoc	zocdoc.com	$223M	TC40 2007	Contestant	Operating	223.00
660	Zula	zulaapp.com	$3.4M	Disrupt SF 2013	Audience choice	Operating	3.40
661	Zumper	zumper.com	$31.5M	Disrupt SF 2012	Finalist	Operating	31.50

440 rows × 7 columns

fundplot = plt.boxplot(COMdata1['Funds_in_million']);
plt.title('Boxplot for Funding')
plt.ylabel('Funds_in_million')
plt.show()

plt.gcf().set_size_inches(15,7)
sns.boxplot(COMdata1['Funds_in_million'],COMdata1['OperatingState']);

C:\Users\Prem\anaconda3\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

upper_fence = fundplot['caps'][1].get_data()[1][1]   # we can use the values from the box plot itself to get the upper fence
upper_fence

22.0

print(f'Number of outliers = {len(COMdata1[COMdata1.Funds_in_million > upper_fence])}')
COMdata1[COMdata1.Funds_in_million > upper_fence]

Number of outliers = 60

	Startup	Product	Funding	Event	Result	OperatingState	Funds_in_million
6	8 Securities	8securities.com	$29M	Disrupt Beijing 2011	Finalist	Operating	29.0
31	Anyclip	anyclip.com	$24M	TC50 2009	Finalist	Operating	24.0
40	Artsy	artsy.net	$50.9M	Disrupt NYC 2010	Contestant	Operating	50.9
49	Badgeville	badgeville.com	$40M	Disrupt SF 2010	Finalist	Acquired	40.0
56	Betterment	betterment.com	$205M	Disrupt NYC 2010	Finalist	Operating	205.0
108	Clickable	clickable.com	$32.5M	TC40 2007	Finalist	Acquired	32.5
113	Cloudflare	cloudflare.com	$182.1M	Disrupt SF 2010	Runner up	Operating	182.1
128	Credit Sesame	creditsesame.com	$35.4M	Disrupt SF 2010	Contestant	Operating	35.4
130	CrowdFlower Inc.	crowdflower.com	$38M	TC50 2009	Contestant	Operating	38.0
132	Cubic Telecom	cubictelecom.com	$37.1M	TC40 2007	Contestant	Operating	37.1
138	DataSift	datasift.com	$72M	Disrupt SF 2010	Finalist	Operating	72.0
139	DataXu	dataxu.com	$64M	TC50 2009	Contestant	Operating	64.0
154	Dropbox	dropbox.com	$1.7B	TC50 2008	Contestant	Operating	1700.0
166	Enigma	enigma.io	$34.6M	Disrupt NYC 2013	Winner	Operating	34.6
172	EverythingMe	everything.me	$35.5M	Disrupt NYC 2011	Contestant	Closed	35.5
179	Famo.us	famo.us	$30.1M	Disrupt SF 2012	Contestant	Operating	30.1
180	Farmigo	farmigo.com	$26M	Disrupt SF 2011	Finalist	Operating	26.0
188	Fitbit	fitbit.com	$66M	TC50 2008	Finalist	Ipo	66.0
191	Flock	flock.com	$28.3M	TC40 2007	Contestant	Acquired	28.3
209	Getaround	getaround.com	$103M	Disrupt NYC 2011	Winner	Operating	103.0
213	Gild	gild.com	$25.9M	Disrupt SF 2010	Contestant	Acquired	25.9
215	Glide	glide.me	$36.5M	Disrupt NYC 2013	Audience choice	Operating	36.5
225	Grockit	grockit.com	$44.7M	TC50 2008	Finalist	Acquired	44.7
231	HackerRank	hackerrank.com	$24.2M	Disrupt SF 2012	Contestant	Operating	24.2
271	Ionic Security	ionicsecurity.com	$122.4M	Disrupt SF 2012	Contestant	Operating	122.4
276	IZEA	izea.com	$34.9M	Disrupt NYC 2010	Contestant	Ipo	34.9
279	Jiff	jiff.com	$67.8M	Disrupt SF 2011	Contestant	Acquired	67.8
282	Kaltura	kaltura.com	$166.1M	TC40 2007	Audience choice	Operating	166.1
302	Layer	layer.com	$42.1M	Disrupt SF 2013	Winner	Operating	42.1
305	LearnVest	learnvest.com	$69M	TC50 2009	Contestant	Acquired	69.0
313	LiveIntent	liveintent.com	$65.1M	Disrupt NYC 2010	Audience choice	Operating	65.1
325	Lystable	lystable.com	$25.1M	Disrupt London 2015	Finalist	Operating	25.1
346	Mint	mint.com	$31.8M	TC40 2007	Winner	Acquired	31.8
389	OrderWithMe	orderwithme.com	$37M	Disrupt Beijing 2011	Winner	Operating	37.0
393	Osmo	playosmo.com	$38.5M	Disrupt SF 2013	Contestant	Operating	38.5
394	Ossia	ossia.com	$25.5M	Disrupt SF 2013	Runner up	Operating	25.5
398	Owlet Baby Care	owletcare.com	$24M	Hardware Battlefield 2014	Runner up	Operating	24.0
427	Postmates	postmates.com	$278M	Disrupt SF 2011	Contestant	Operating	278.0
432	Prism Skylabs	prism.com	$24M	Disrupt SF 2011	Runner up	Operating	24.0
435	PubMatic	pubmatic.com	$63M	TC40 2007	Contestant	Operating	63.0
460	Roadie	roadie.com	$25M	Disrupt NYC 2014	Audience choice	Operating	25.0
471	SeatGeek	seatgeek.com	$160M	TC50 2009	Contestant	Operating	160.0
546	StyleSeat	styleseat.com	$40M	Disrupt NYC 2011	Contestant	Operating	40.0
555	Symphony Commerce	symphonycommerce.com	$47.4M	Disrupt NYC 2011	Contestant	Operating	47.4
560	Talkdesk	talkdesk.com	$24.5M	Disrupt NYC 2012	Contestant	Operating	24.5
581	TouchPal	touchpal.com	$25M	Disrupt Beijing 2011	Finalist	Operating	25.0
593	TrueCar	truecar.com	$332.4M	TC50 2008	Contestant	Ipo	332.4
598	UberConference	uberconference.com	$35M	Disrupt NYC 2012	Winner	Operating	35.0
606	Upwork	upwork.com	$168.8M	TC50 2009	Audience choice	Operating	168.8
615	VideoSurf	videosurf.com	$28M	TC50 2008	Contestant	Acquired	28.0
625	Voxy	voxy.com	$30.8M	Disrupt SF 2010	Contestant	Operating	30.8
643	Xobni	yahoo.com	$41.8M	TC40 2007	Contestant	Acquired	41.8
644	Yammer	yammer.com	$142M	TC50 2008	Winner	Acquired	142.0
647	Yext	yext.com	$117.8M	TC50 2009	Contestant	Ipo	117.8
649	YouNow	younow.com	$26M	Disrupt SF 2011	Contestant	Operating	26.0
650	YourMechanic	yourmechanic.com	$28M	Disrupt SF 2012	Winner	Operating	28.0
654	ZEFR	zefr.com	$62.1M	Disrupt NYC 2010	Contestant	Operating	62.1
656	Zenefits	zenefits.com	$583.6M	Disrupt NYC 2013	Finalist	Operating	583.6
659	Zocdoc	zocdoc.com	$223M	TC40 2007	Contestant	Operating	223.0
661	Zumper	zumper.com	$31.5M	Disrupt SF 2012	Finalist	Operating	31.5

COMdata1.drop(COMdata1[COMdata1.Funds_in_million > upper_fence].index,inplace=True)

COMdata1.shape

(380, 7)

plt.gcf().set_size_inches(15,7)
sns.boxplot(COMdata1['Funds_in_million'],COMdata1['OperatingState']);

C:\Users\Prem\anaconda3\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

COMdata1.OperatingState.value_counts()

Operating    269
Closed        56
Acquired      55
Name: OperatingState, dtype: int64

sns.distplot(COMdata1.Funds_in_million)
plt.title('Distribution of funds raised across all companies')
plt.show()

C:\Users\Prem\anaconda3\lib\site-packages\seaborn\distributions.py:2557: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

sns.set_theme(style="darkgrid")
ax1 = sns.barplot(x='OperatingState', y='Funds_in_million', data=COMdata1, palette='bright')  # barplot

fig, ax = plt.subplots(1,2)
fig.set_figheight(5)
fig.set_figwidth(15)

sns.distplot(COMdata1.loc[COMdata1.OperatingState == 'Operating','Funds_in_million'],ax=ax[0])
sns.distplot(COMdata1.loc[COMdata1.OperatingState == 'Closed','Funds_in_million'],ax=ax[1])

ax[0].set_title('Funds raised by the companies still operating')
ax[1].set_title('Funds raised by companies that got closed')
plt.show()

C:\Users\Prem\anaconda3\lib\site-packages\seaborn\distributions.py:2557: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\Prem\anaconda3\lib\site-packages\seaborn\distributions.py:2557: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

Statistical analysis:

First test,

Null hypothesis (Ho) : There is no difference between the two means

Alternate hypothesis (Ha) : There is significant difference between the two means

from statsmodels.stats.weightstats import ztest

sample1 = COMdata1.loc[COMdata1.OperatingState == 'Operating', 'Funds_in_million']
sample2 = COMdata1.loc[COMdata1.OperatingState =='Closed', 'Funds_in_million']

alpha = 0.05   # Let's consider a significance level of 5%

test_statistic, p_value = ztest(sample1, sample2)

if p_value <= alpha:
    print(f'Since the p-value, {round(p_value, 3)} < {alpha} (alpha) the difference is significant and we reject the Null hypothesis')
else:
    print(f'''\t Since the p-value, {round(p_value,3)} > {alpha} (alpha) the difference is not significant and,
    \t we fail to reject the Null hypothesis''')

	 Since the p-value, 0.172 > 0.05 (alpha) the difference is not significant and,
    	 we fail to reject the Null hypothesis

From the test above, There is no difference between the two means. Hence no evidance to state the companies that have raised more money tend to suceed more or vice-versa

COMdata2 = COMdata1.copy()
COMdata2.head()

	Startup	Product	Funding	Event	Result	OperatingState	Funds_in_million
1	3DLT	3dlt.com	$630K	Disrupt NYC 2013	Contestant	Closed	0.63
3	3Dprintler	3dprintler.com	$1M	Disrupt NY 2016	Audience choice	Operating	1.00
5	5to1	5to1.com	$19.3M	TC50 2009	Contestant	Acquired	19.30
10	AdhereTech	adheretech.com	$1.8M	Hardware Battlefield 2014	Contestant	Operating	1.80
11	AdRocket	adrocket.com	$1M	TC50 2008	Contestant	Closed	1.00

COMdata2.Result.value_counts()

Contestant         281
Finalist            51
Audience choice     18
Winner              16
Runner up           14
Name: Result, dtype: int64

winners = COMdata2.Result.value_counts()[1:].sum()
contestants = COMdata2.Result.value_counts()['Contestant']

contestants_operating = COMdata2.OperatingState[COMdata2.Result == 'Contestant'].value_counts().loc['Operating']
winners_operating = COMdata2.OperatingState[COMdata2.Result != 'Contestant'].value_counts().loc['Operating']

A=winners_operating/winners
B=contestants_operating/contestants

print('Percentage of winners that are still operating',round(A,3))
print('Percentage of contestants that are still operating',round(B,3))

Percentage of winners that are still operating 0.768
Percentage of contestants that are still operating 0.687

• There is some difference between the proportion operational companies in the two categories, but let's see if the differnce is significant
• There are two ways we can check if the difference is significant
  • Z-test for proportions
  • Chi-square test
• We shall perform z-test in this case, however, do experiment with Chi-square test and observe if the p-value from both tests gives the same conclusion or not

Null hypothesis (Ho): The proportion of companies that are operating is the same in both categories - winners and contestants

Alternative hypothesis (Ha): The proportion of companies that are operating is significantly different from each other, among the two categories

from statsmodels.stats.proportion import proportions_ztest

test_statistic, p_value = proportions_ztest([contestants_operating, winners_operating], [contestants, winners])

if p_value <= alpha:
    print(f'Since the p-value, {round(p_value, 3)} < {alpha} (alpha) the difference is significant and we reject the Null hypothesis')
else:
    print(f'''\t Since the p-value, {round(p_value,3)} > {alpha} (alpha) the difference is not significant and,
    \t we fail to reject the Null hypothesis''')

	 Since the p-value, 0.128 > 0.05 (alpha) the difference is not significant and,
    	 we fail to reject the Null hypothesis

Conclusion:

• The amount of funds a company raises is not a significant factor in deciding if the company will remain operational or close down
• Winners have proven to remain operational more so, than the companies that came out only as contestants

COMdata2.Event.value_counts()

TC50 2008                    25
TC40 2007                    22
Disrupt NY 2015              21
Disrupt NYC 2013             19
Disrupt SF 2015              19
TC50 2009                    19
Disrupt NYC 2012             19
Disrupt SF 2011              19
Disrupt SF 2013              19
Disrupt SF 2014              19
Disrupt SF 2016              17
Disrupt NY 2016              16
Disrupt SF 2012              15
Disrupt NYC 2014             15
Disrupt NYC 2011             15
Disrupt SF 2010              13
Hardware Battlefield 2014    12
Hardware Battlefield 2016    12
Disrupt London 2015          11
Hardware Battlefield 2015    10
Disrupt NYC 2010             10
Disrupt EU 2014              10
Disrupt London 2016          10
Disrupt EU 2013               9
Disrupt Beijing 2011          4
Name: Event, dtype: int64

COMdata2[COMdata2.Event.apply(lambda x: 'Disrupt' in x)].Event.value_counts()

Disrupt NY 2015         21
Disrupt SF 2011         19
Disrupt NYC 2013        19
Disrupt NYC 2012        19
Disrupt SF 2014         19
Disrupt SF 2015         19
Disrupt SF 2013         19
Disrupt SF 2016         17
Disrupt NY 2016         16
Disrupt SF 2012         15
Disrupt NYC 2014        15
Disrupt NYC 2011        15
Disrupt SF 2010         13
Disrupt London 2015     11
Disrupt London 2016     10
Disrupt NYC 2010        10
Disrupt EU 2014         10
Disrupt EU 2013          9
Disrupt Beijing 2011     4
Name: Event, dtype: int64

events = COMdata2[COMdata2.Event.apply(lambda x: 'Disrupt' in x and int(x[-4:]) > 2012)].Event
events

1         Disrupt NYC 2013
3          Disrupt NY 2016
13         Disrupt SF 2015
14     Disrupt London 2016
16         Disrupt SF 2015
              ...         
635        Disrupt NY 2015
641       Disrupt NYC 2013
642        Disrupt SF 2014
646    Disrupt London 2015
660        Disrupt SF 2013
Name: Event, Length: 185, dtype: object

NYE = COMdata2.loc[events[events.apply(lambda x: 'NY' in x)].index,'Funds_in_million']
SFE = COMdata2.loc[events[events.apply(lambda x: 'SF' in x)].index,'Funds_in_million']
EUE = COMdata2.loc[events[events.apply(lambda x: 'EU' in x or 'London' in x)].index,'Funds_in_million']
print(len(NYE), len(SFE), len(EUE))

71 74 40

• The sample sizes are different across the three categories and it is okay to perform ANOVA on samples of different sizes

Null Hypothesis(Ho): Average funds raised by companies across three cities are the same

Alternative Hypothesis(Ha): Average funds raised by companies across three cities are the different

plt.figure(figsize=(15,6))
sns.distplot(NYE, color = 'Red', label = 'NY')
sns.distplot(SFE, color = 'Gold', label = 'SF')
sns.distplot(EUE, color = 'blue', label = 'EU')
plt.legend()
plt.show()

C:\Users\Prem\anaconda3\lib\site-packages\seaborn\distributions.py:2557: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\Prem\anaconda3\lib\site-packages\seaborn\distributions.py:2557: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\Prem\anaconda3\lib\site-packages\seaborn\distributions.py:2557: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

from scipy.stats import f_oneway


stat, p_value = f_oneway(NYE, SFE, EUE)

if p_value <= alpha:
    print(f'Since the p-value, {round(p_value, 3)} < {alpha} (alpha) the difference is significant and we reject the Null hypothesis')
else:
    print(f'''\t Since the p-value, {round(p_value,3)} > {alpha} (alpha) the difference is not significant and,
    \t we fail to reject the Null hypothesis''')

	 Since the p-value, 0.628 > 0.05 (alpha) the difference is not significant and,
    	 we fail to reject the Null hypothesis

From the ANOVA test

• The distribution of funds raised by the companies across the three regions is the same
• We found no evidence to say companies participating in certain regions have funds either significantly on the higher side or on the lower side

---------------------------------------- THANK YOU -----------------------------------